Document Open Access Logo

Brief Announcement: Zero-Knowledge Protocols for Search Problems

Authors Ben Berger, Zvika Brakerski

PDF
Thumbnail PDF

File

LIPIcs.ICALP.2018.105.pdf
  • Filesize: 246 kB
  • 5 pages

Document Identifiers

Author Details

Ben Berger
  • Weizmann Institute of Science, Rehovot, Israel
Zvika Brakerski
  • Weizmann Institute of Science, Rehovot, Israel

Funding

Supported by the Israel Science Foundation (Grant No. 468/14), Binational Science Foundation (Grants No. 2016726, 2014276), and by the European Union Horizon 2020 Research and Innovation Program via ERC Project REACT (Grant 756482) and via Project PROMETHEUS (Grant 780701).

Cite As Get BibTex

Ben Berger and Zvika Brakerski. Brief Announcement: Zero-Knowledge Protocols for Search Problems. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 105:1-105:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ICALP.2018.105

Abstract

We consider natural ways to extend the notion of Zero-Knowledge (ZK) Proofs beyond decision problems. Specifically, we consider search problems, and define zero-knowledge proofs in this context as interactive protocols in which the prover can establish the correctness of a solution to a given instance without the verifier learning anything beyond the intended solution, even if it deviates from the protocol.
The goal of this work is to initiate a study of Search Zero-Knowledge (search-ZK), the class of search problems for which such systems exist. This class trivially contains search problems where the validity of a solution can be efficiently verified (using a single message proof containing only the solution). A slightly less obvious, but still straightforward, way to obtain zero-knowledge proofs for search problems is to let the prover send a solution and prove in zero-knowledge that the instance-solution pair is valid. However, there may be other ways to obtain such zero-knowledge proofs, and they may be more advantageous.
In fact, we prove that there are search problems for which the aforementioned approach fails, but still search zero-knowledge protocols exist. On the other hand, we show sufficient conditions for search problems under which some form of zero-knowledge can be obtained using the straightforward way.

Subject Classification

ACM Subject Classification
  • Theory of computation → Interactive proof systems
  • Theory of computation → Cryptographic protocols
Keywords
  • Zero-Knowledge
  • Search Problems
  • Interactive Proofs

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Amos Beimel, Paz Carmi, Kobbi Nissim, and Enav Weinreb. Private approximation of search problems. In Jon M. Kleinberg, editor, Proceedings of the 38th Annual ACM Symposium on Theory of Computing, Seattle, WA, USA, May 21-23, 2006, pages 119-128. ACM, 2006. URL: http://dx.doi.org/10.1145/1132516.1132533.
  2. Michael Ben-Or, Shafi Goldwasser, and Avi Wigderson. Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In Proceedings of the 20th Annual ACM Symposium on Theory of Computing, May 2-4, 1988, Chicago, Illinois, USA, pages 1-10, 1988. URL: http://dx.doi.org/10.1145/62212.62213.
  3. David Chaum, Claude Crépeau, and Ivan Damgård. Multiparty unconditionally secure protocols (extended abstract). In Proceedings of the 20th Annual ACM Symposium on Theory of Computing, May 2-4, 1988, Chicago, Illinois, USA, pages 11-19, 1988. URL: http://dx.doi.org/10.1145/62212.62214.
  4. Ivan Damgård, Oded Goldreich, Tatsuaki Okamoto, and Avi Wigderson. Honest verifier vs dishonest verifier in public coin zero-knowledge proofs. In Don Coppersmith, editor, Advances in Cryptology - CRYPTO '95, 15th Annual International Cryptology Conference, Santa Barbara, California, USA, August 27-31, 1995, Proceedings, volume 963 of Lecture Notes in Computer Science, pages 325-338. Springer, 1995. URL: http://dx.doi.org/10.1007/3-540-44750-4_26.
  5. Joan Feigenbaum, Yuval Ishai, Tal Malkin, Kobbi Nissim, Martin Strauss, and Rebecca N. Wright. Secure multiparty computation of approximations. In Fernando Orejas, Paul G. Spirakis, and Jan van Leeuwen, editors, Automata, Languages and Programming, 28th International Colloquium, ICALP 2001, Crete, Greece, July 8-12, 2001, Proceedings, volume 2076 of Lecture Notes in Computer Science, pages 927-938. Springer, 2001. URL: http://dx.doi.org/10.1007/3-540-48224-5_75.
  6. Eran Gat and Shafi Goldwasser. Probabilistic search algorithms with unique answers and their cryptographic applications. Electronic Colloquium on Computational Complexity (ECCC), 18:136, 2011. URL: http://eccc.hpi-web.de/report/2011/136.
  7. Oded Goldreich, Shafi Goldwasser, and Dana Ron. On the possibilities and limitations of pseudodeterministic algorithms. In Robert D. Kleinberg, editor, Innovations in Theoretical Computer Science, ITCS '13, Berkeley, CA, USA, January 9-12, 2013, pages 127-138. ACM, 2013. URL: http://dx.doi.org/10.1145/2422436.2422453.
  8. Oded Goldreich, Silvio Micali, and Avi Wigderson. How to play any mental game or a completeness theorem for protocols with honest majority. In STOC, pages 218-229, 1987. Google Scholar
  9. Oded Goldreich, Amit Sahai, and Salil P. Vadhan. Honest-verifier statistical zero-knowledge equals general statistical zero-knowledge. In Jeffrey Scott Vitter, editor, Proceedings of the Thirtieth Annual ACM Symposium on the Theory of Computing, Dallas, Texas, USA, May 23-26, 1998, pages 399-408. ACM, 1998. URL: http://dx.doi.org/10.1145/276698.276852.
  10. Oded Goldreich, Amit Sahai, and Salil P. Vadhan. Can statistical zero knowledge be made non-interactive? or on the relationship of SZK and NISZK. In Michael J. Wiener, editor, Advances in Cryptology - CRYPTO '99, 19th Annual International Cryptology Conference, Santa Barbara, California, USA, August 15-19, 1999, Proceedings, volume 1666 of Lecture Notes in Computer Science, pages 467-484. Springer, 1999. URL: http://dx.doi.org/10.1007/3-540-48405-1_30.
  11. Oded Goldreich and Salil P. Vadhan. Comparing entropies in statistical zero knowledge with applications to the structure of SZK. In Proceedings of the 14th Annual IEEE Conference on Computational Complexity, Atlanta, Georgia, USA, May 4-6, 1999, page 54. IEEE Computer Society, 1999. URL: http://dx.doi.org/10.1109/CCC.1999.766262.
  12. Shafi Goldwasser and Ofer Grossman. Perfect bipartite matching in pseudo-deterministic RNC. Electronic Colloquium on Computational Complexity (ECCC), 22:208, 2015. URL: http://eccc.hpi-web.de/report/2015/208.
  13. Shafi Goldwasser and Ofer Grossman. Bipartite perfect matching in pseudo-deterministic NC. In Ioannis Chatzigiannakis, Piotr Indyk, Fabian Kuhn, and Anca Muscholl, editors, 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, July 10-14, 2017, Warsaw, Poland, volume 80 of LIPIcs, pages 87:1-87:13. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2017. URL: http://dx.doi.org/10.4230/LIPIcs.ICALP.2017.87.
  14. Shafi Goldwasser, Ofer Grossman, and Dhiraj Holden. Pseudo-deterministic proofs. In Anna R. Karlin, editor, 9th Innovations in Theoretical Computer Science Conference, ITCS 2018, January 11-14, 2018, Cambridge, MA, USA, volume 94 of LIPIcs, pages 17:1-17:18. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2018. URL: http://dx.doi.org/10.4230/LIPIcs.ITCS.2018.17.
  15. Shafi Goldwasser, Silvio Micali, and Charles Rackoff. The knowledge complexity of interactive proof systems. SIAM J. Comput., 18(1):186-208, 1989. URL: http://dx.doi.org/10.1137/0218012.
  16. Ofer Grossman. Finding primitive roots pseudo-deterministically. Electronic Colloquium on Computational Complexity (ECCC), 22:207, 2015. URL: http://eccc.hpi-web.de/report/2015/207.
  17. Shai Halevi, Robert Krauthgamer, Eyal Kushilevitz, and Kobbi Nissim. Private approximation of np-hard functions. In Jeffrey Scott Vitter, Paul G. Spirakis, and Mihalis Yannakakis, editors, Proceedings on 33rd Annual ACM Symposium on Theory of Computing, July 6-8, 2001, Heraklion, Crete, Greece, pages 550-559. ACM, 2001. URL: http://dx.doi.org/10.1145/380752.380850.
  18. Tatsuaki Okamoto. On relationships between statistical zero-knowledge proofs. In Gary L. Miller, editor, Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing, Philadelphia, Pennsylvania, USA, May 22-24, 1996, pages 649-658. ACM, 1996. URL: http://dx.doi.org/10.1145/237814.238016.
  19. Amit Sahai and Salil P. Vadhan. A complete problem for statistical zero knowledge. J. ACM, 50(2):196-249, 2003. URL: http://dx.doi.org/10.1145/636865.636868.
  20. Andrew Chi-Chih Yao. Protocols for secure computations (extended abstract). In FOCS, pages 160-164, 1982. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact